Problem: $\dfrac{ -8n + 6p }{ 3 } = \dfrac{ 5n - 4q }{ -5 }$ Solve for $n$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -8n + 6p }{ {3} } = \dfrac{ 5n - 4q }{ -5 }$ ${3} \cdot \dfrac{ -8n + 6p }{ {3} } = {3} \cdot \dfrac{ 5n - 4q }{ -5 }$ $-8n + 6p = {3} \cdot \dfrac { 5n - 4q }{ -5 }$ Multiply both sides by the right denominator. $-8n + 6p = 3 \cdot \dfrac{ 5n - 4q }{ -{5} }$ $-{5} \cdot \left( -8n + 6p \right) = -{5} \cdot 3 \cdot \dfrac{ 5n - 4q }{ -{5} }$ $-{5} \cdot \left( -8n + 6p \right) = 3 \cdot \left( 5n - 4q \right)$ Distribute both sides $-{5} \cdot \left( -8n + 6p \right) = {3} \cdot \left( 5n - 4q \right)$ ${40}n - {30}p = {15}n - {12}q$ Combine $n$ terms on the left. ${40n} - 30p = {15n} - 12q$ ${25n} - 30p = -12q$ Move the $p$ term to the right. $25n - {30p} = -12q$ $25n = -12q + {30p}$ Isolate $n$ by dividing both sides by its coefficient. ${25}n = -12q + 30p$ $n = \dfrac{ -12q + 30p }{ {25} }$